Polymer Dynamics in Repton Model at Large Fields

TL;DR

This paper investigates the behavior of polymer chains under large external fields using the Rubinstein-Duke repton model, revealing how drift velocity varies with polymer type, size, and charge distribution through theoretical and numerical methods.

Contribution

It introduces a diagrammatic approach and applies density-matrix renormalization group techniques to analyze polymer drift velocities in large fields, highlighting differences based on polymer charge composition.

Findings

Drift velocity of polyelectrolytes decreases exponentially with field strength.

Polyampholytes' drift velocity is independent of chain size.

Neutral blocks determine the drift velocity in mixed-charge polymers.

Abstract

Polymer dynamics at large fields in Rubinstein-Duke repton model is investigated theoretically. Simple diagrammatic approach and analogy with asymmetric simple exclusion models are used to analyze the reptation dynamics of polymers. It is found that for polyelectrolytes the drift velocity decreases exponentially as a function of the external field with an exponent depending on polymer size and parity, while for polyampholytes the drift velocity is independent of polymer chain size. However, for polymers, consisting of charged and neutral blocks, the drift velocity approaches the constant limit which is determined by the size of the neutral block. The theoretical arguments are supported by extensive numerical calculations by means of density-matrix renormalization group techniques.